Does 的话 in 这句常挂在嘴边上的话，便点点头答应了 create "If~" subclause?

Question

In the following sentence:

小姐见他有点儿犹豫，便有声有色地向他介绍吸粉的妙处。这时，他想起了，“在社会上混，什么都得尝试尝试” 这句常挂在嘴边上的话，便点点头答应了。

Regarding this usage of 的话, the first I came up with is the use of "If ~, then ..." structure. But this lacks the two fundamental points:

• It lacks 如果. But I know it has no problem grammatically, and the omission of 如果 is common.

• It lacks 就 in the main clause. If subclause is 如果～的话, then the main clause needs 就, 那, or 那么.

So my questions are:

• Is my understanding that the usage of 的话 here is "If ~"?

• If it is correct, is it acceptable to use 便 in the main clause instead of 就 or 那?

The sentence also sounds a bit awkward, meaning:

If this sentence always hangs on the mouse, (he) nodded the head.

Which sounds a bit awkward. "As long/far as" or just use "so" sound more natural for me, like:

This sentence always hangs on the mouse, so he nodded the head.

So how does 的话 work here and what is the correct meaning of the sentence?

Answer 1

Your example doesn't suit the question. The break down of this sentence is

[这句常挂在嘴边上的 (adjectival phrase)] modifies the noun [话]

"这句常挂在嘴边上的[话]" = "[the words] that is spoken often (by people)"

As for the usage of the set phrase [的话], it functions as [if~], as you described

If it is correct, is it acceptable to use 便 in the main clause instead of 就 or 那?

Yes, depend on the context, [如果～的话] can be followed by different conjunctions like 便, 就, 那

A correct example of [～的话]:

"不想吃[1. 的话][2. 就]不要勉強" - "[1. If] you don't want to eat, [2. then] don't force yourself"

'就' here can be replaced by"便" or "那就"

Answer 2

No, it's not a if...then... structure here.

话 here is used as its literal meaning， words or sentence.

The main clause is actually 他想起了话. And the 话 he recalled was “在社会上混，什么都得尝试尝试”, which always hangs on his mouth(implying he often says that sentence.)

他想起了，<“在社会上混，什么都得尝试尝试”> {这句常挂在嘴边上的}话

So when that sentence came into his mind, 便点点头答应了 he nodded and agree to do it.